Winchester m70 sporting sharpshooter problem

I just picked up a sporting sharpshooter but have not had a chance to shoot it. I just started putting together the first loads and when I measured the distance to the lands , the resized case was very difficult to remove. I sorted through my resized brass and the majority fit very tight to the chamber. I tried new brass and had no problem. The resized brass is hitting in the center of the case which I think is caused by small or low end of the chamber diameter. I would like to get your thoughts on this.